Highest Common Factor of 198, 709, 167 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 198, 709, 167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 198, 709, 167 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 198, 709, 167 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 198, 709, 167 is 1.
HCF(198, 709, 167) = 1
HCF of 198, 709, 167 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 198, 709, 167 is 1.
Highest Common Factor of 198,709,167 is 1
Step 1: Since 709 > 198, we apply the division lemma to 709 and 198, to get
709 = 198 x 3 + 115
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 115 and 198, to get
198 = 115 x 1 + 83
Step 3: We consider the new divisor 115 and the new remainder 83, and apply the division lemma to get
115 = 83 x 1 + 32
We consider the new divisor 83 and the new remainder 32,and apply the division lemma to get
83 = 32 x 2 + 19
We consider the new divisor 32 and the new remainder 19,and apply the division lemma to get
32 = 19 x 1 + 13
We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get
19 = 13 x 1 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 198 and 709 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(32,19) = HCF(83,32) = HCF(115,83) = HCF(198,115) = HCF(709,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 167 > 1, we apply the division lemma to 167 and 1, to get
167 = 1 x 167 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 167 is 1
Notice that 1 = HCF(167,1) .
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Frequently Asked Questions on HCF of 198, 709, 167 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 198, 709, 167?
Answer: HCF of 198, 709, 167 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 198, 709, 167 using Euclid's Algorithm?
Answer: For arbitrary numbers 198, 709, 167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.